Question
What additional information will allow you to prove the triangles congruent by the HL Theorem?Triangles A B C and D E C are shown with a common vertex at C at the intersection of A E and B D. Side A B is congruent to side D E. Angles A C B and D C E are right angles.
(1 point)
Responses
angleA congruent toangleE
Image with alt text: angle A Image with alt text: congruent to Image with alt text: angle E
mangleBCE = 90
m Image with alt text: angle BCE = 90
Modifying above upper A upper C with barcongruent toModifying above upper D upper C with bar
Image with alt text: Modifying above upper A upper C with bar Image with alt text: congruent to Image with alt text: Modifying above upper D upper C with bar
Modifying above upper A upper C with barcongruent toModifying Above Upper B Upper D with bar
Image with alt text: Modifying above upper A upper C with bar Image with alt text: congruent to Image with alt text: Modifying Above Upper B Upper D with bar
Image with alt text: Modifying above upper A upper C with bar Image with alt text: congruent to Image with alt text: Modifying Above Upper B Upper D with bar
To prove the triangles ABD and DEC congruent by the HL (Hypotenuse-Leg) Theorem, we need to show that the hypotenuse AB is congruent to the hypotenuse DE, and the leg AC is congruent to the leg DC.
In this case, we are given that AB is congruent to DE (side A B congruent to side D E) and that angles ACB and DCE are right angles.
To prove that the hypotenuses are congruent, we use the fact that side AB is congruent to side DE.
To prove that the legs are congruent, we use the fact that angles ACB and DCE are right angles. By definition, right angles are congruent. Therefore, angle ACB is congruent to angle DCE.
Therefore, the additional information we need to prove the triangles congruent by the HL Theorem is that angle ACB is congruent to angle DCE.